Theorem mulcomi 8113

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
mulcomi	|- ( A x. B ) = ( B x. A )

Proof of Theorem mulcomi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcom 8089	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )
4	1, 2, 3	mp2an 426	1 |- ( A x. B ) = ( B x. A )

Syntax hints:   = wceq 1373   e. wcel 2178  (class class class)co 5967   CCcc 7958   x. cmul 7965

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-mulcom 8061

This theorem is referenced by:  mulcomli  8114  8th4div3  9291  numma2c  9584  nummul2c  9588  9t11e99  9668  binom2i  10830  fac3  10914  tanval2ap  12139  pockthi  12796  decsplit1  12866  decsplit  12867  sincosq4sgn  15416  2logb9irrALT  15561  2lgsoddprmlem2  15698  2lgsoddprmlem3d  15702